The method and system disclosed herein relate to determining threshold voltage variations in field effect transistors (FETs).
As FETs continue to be scaled in size, the impact of random threshold voltage variation on FET performance increases and the ability to measure such random threshold voltage variation becomes more difficult. For example, the total random threshold voltage variation between a pair of adjacent FETs, which are identical in layout (e.g., same channel length and same channel width), will be equal to the sum of both a correlated random threshold voltage variation and an uncorrelated random threshold voltage variation. The correlated random threshold voltage variation (also referred to herein as a systematic random threshold voltage variation) refers to a variation wherein the variation direction away from a nominal threshold voltage value will be the same for both of the FETs in the pair. For example, the gate dielectric thickness may vary from chip to chip such that the threshold voltages of the FETs in the pair may both be greater than or less than the nominal threshold voltage value. An uncorrelated random threshold voltage variation refers to a variation wherein the variation direction away from the nominal threshold voltage value can be the same or different (i.e., entirely random) for the FETs in the pair. For example, random dopant fluctuations (RDFs) may occur across a chip such that the threshold voltage of either of the FETs in the pair may be greater than or less than the nominal threshold voltage value. Thus, the correlated random variation does not contribute to the threshold voltage mismatch between the FETs in the pair, but the uncorrelated variation does. Since threshold voltage matching between FETs is critical in many circuits (e.g., static random access memory (SRAM) circuits, dynamic random access memory (DRAM) circuit, etc.), it is important during testing to properly determine not only the uncorrelated threshold voltage variation that leads to threshold voltage mismatch, but also the correlated threshold voltage variation that does not. However, current testing techniques do not account for the correlated threshold voltage variation and, thereby have limited accuracy. Similarly, techniques are also known for determining a difference between the average threshold voltages of two FETs, which differ in layout only with respect to their channel widths, in order to characterize the width scaling relation (i.e., to determine changes in threshold voltage as a function of channel width). However, such techniques do not account for any contribution from uncorrelated random threshold voltage variations and, thereby also have limited accuracy.